Given two intersecting line segments, the angle they form at their
intersection, the coordinates of one endpoint and those of the
intersection, and the length of one of the line segments, how do you
determine the coordinates of the remaining endpoint?

How can I find the coordinates of the point A of triangle ABC if B lies
on the line 3y = 4x, C lies on the line y = 0, the line BC passes through
(2/3,2/3) and AOBC forms a rhombus (where O is the origin)?

If (X,Y) is a point in the 1st quadrant on the unit circle and m is the
slope of the line passing through (X,Y) and the point (0,-1), how can I
express the coordinates (X,Y) in terms of m? Can this be used to generate
Pythagorean triples?